08 March 2011

Standard Model Still Probably Broken

The continues to be strong evidence that the Standard Model theory prediction for CP violations with higher generation fermions is deeply off the mark and the Standard Model is missing something important.

Either that, or our approximations of the QCD background against which these predictions are being made is off. We have what we believe to be the perfectly accurate equations of the strong force and reasonably accurate determinations of all of its constants, but we aren't able to solve the math in particular situations exactly with nice clean equations - we have to either approximate the results using the early terms of an infinite series approximation that doesn't converge very quickly, or or approximate the results by making exact calculations using a model in which space-time is lumpier than it is in real life (i.e. using chunks much larger than the Plank distance) called Lattice QCD.

It is also worth noting at this point that QCD equations actually have a term which could introduce CP violations via the strong force, rather than the weak force interactions measured in the results mentioend above. But, all experimental evidence to date has failed to find a strong force CP violation, implying that the constant by which that QCD term is multiplied is probably zero.

QCD equations have thus far been calculated to low single digit percentage accuracy, which while not great, should be sufficient in the experiements showing unexpectedly large CP violations in top-antitop quark pair production (which are on the order of forty something percent off from the expected value), unless CP violations (which are equivalent to time symmetry violations) are especially sensitive to the approximation method used.

Assuming that this is more than a flaw in the QCD calculations, the exciting question is what LHC will tell us about the beyond the Standard Model new physics that apparently exist.

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One place we are unlikely to find fault with current theories is Lorentz Invariance, which was proved in 2002 (a beautiful result) to be equivalent with some very minimal assumptions (the lack of negative energy in the universe is probably the most notable), to the proposition that CPT violations do not exist:

[T]he Fermi satellite has shown that the Lorentz violation even at the Planck scale must be much smaller than O(100%). . .. the Lorentz violation at the Planck scale - by the 1/M_{Pl} operators - has to be smaller than 85 x 10^{-15}: the key symmetry is more accurate than a part per trillion.

Other than Planck's constant itself, there is pretty much no other proposition in physics that has been confirmed experimentally at anything close to the Planck scale. Prior experimental efforts to constrain the scale of any such violations as of 2008 is found here.

The Lorentz invariance principle basically holds that activities within a lab with respect to each other are not influenced by the orientation of the lab or its motion with respect to anything else in the universe. Thus, while there is definitely an arrow of time in some quantum pheneomena, with the laws not producing identical results when run forward and backward in time, the way that this difference plays out is extremely well constrained by CPT symmetry.

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Marco Frasca of Gauge Connection blog fame also has a paper updated as of December 2010 which argues that if "mass generation for Yang-Mills theory" (which is the theory underlying QCD, the quantum field theory of the strong force), is "the same in QCD as in the Standard Model, this implies that Higgs particle must be supersymmetric." Like all papers in physics, the mere fact that a pre-print has been found on arxiv does not mean that the conclusion is true, peer review could reveal flaw, for example, and a considerable number of assumptions go into it as well. But, deriving supersymmetry from the Standard Model itself with only very minimal assumptions (primarily that QCD and other parts of the Standard Model generate mass in the same way) is impressive.

On the other hand, the paper really only dervives a toy model of a realistic SUSY theory: "this mechanism, per se, is able to give to all the particles of the theory an identical mass while the coupling are also properly fixed. So, mass differences can only be understood through the mechanism that eventually breaks supersymmetry." The general line of reasoning in the paper appears to be part of the same research program as Walking Technicolor (see also here and here), and arriving at a conclusion that looks remarkably like Technicolor competitor for beyond the Standard Model physics, SUSY.

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Finally, new measurements of neutrino masses are suggesting that what we used to think of as "anti-neutrinos" may in fact be something quite different called "mirror neutrinos." This interpretation avoids a CPT violation associated with the fact that what we used to think we anti-neutrinos have a slightly different mass than mirror neutrinos, despite the fact that at first, after "the release of the MINOS results, many theorists were wondering about the possibility of CPT violation in the neutrino sector." This is interesting too:

The MINOS experiment has observed distinct masses for neutrinos and the so called antineutrinos, which we now call mirror neutrinos. In preliminary results released in 2010, MINOS claim that the total difference in masses squared for neutrinos is around 0.00232 eV2, while for mirror neutrinos it is 0.00336 eV2. Given our new mirror particle zoo, can we say anything about these numbers?

The ordinary neutrinos come in three possible mass states. In 2006, Carl Brannen fitted these three masses to a simple formula, resembling the Koide formula for the three charged lepton masses. First discovered by Yoshio Koide in 1981, this exact relation between the masses of the electron, muon and tau particles was used to predict the tau mass from the more accurately known electron and muon masses. The prediction was correct, and the formula remains in agreement with experimental results. Brannen’s prediction for the neutrino masses was based on the observation that the Koide formula is expressed in terms of a certain matrix . . .[derived from a mathematical manipulation of the] square roots of the three masses. . . . [related to] two elementary Pauli spin operators. The neutrino scale is selected so that the sum of mass squares is around 0.00232 eV2, as observed. Ignoring the choice of mass units, there are two remaining parameters in the neutrino matrix. One parameter is identical to the charged lepton case. The single remaining parameter appears to differ from the charged lepton case by π/12. That is, there is a complex phase parameter of exp(2i/9) for the charged leptons, and exp(2i/9+ πi/12) for the neutrinos. . . . For the equal mass charged leptons and antileptons, the phases exp(±2i/9) give equal masses. . . . The neutrino phase now has two sign components, so we may double the allowed mass sets for the neutral particles by choosing a sign mismatch, as in exp(2i/9- πi/12). With this phase, at the same scale as the neutrinos, the difference of mass squares for the mirror neutrinos is around 0.00336 eV2, as observed.

The mirror mass prediction corresponding to the lightest neutrino mass is now 0.00117 eV. . . . the thermal equivalent of 0.00117 eV under the law for black body radiation is 2.73K, which is precisely the temperature of the cosmic microwave background.

The mass formula in turn, has roots in a 2005 preon theory in which "Bilson-Thompson proposed to map the first Standard Model generation (and the gauge bosons) onto three-strand braids. . . . Bilson-Thompson did not use all possible braids, and under ]post author] Sheppeard’s mapping (of braids to matrices) the unused braids are assigned specific quantum numbers, including their mass. The “mirror neutrino” with a mass of 0.00117 eV corresponds to one of these unused braids."

As always, the interpretations are somewhat speculative. The author's blog exploring these ideas is here.

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This is pretty amazing stuff.

As I noted in earlier posts, we are discovering that the Standard Model QCD equations predict a massive spin zero particle called a glueball whose mass declines as a gains momentum (the formula is apparently m^2+cp^2 where c is the speed of light and p is momentum), that you've never heard of in low energy settings.

Also, apparently, what we used to think were anti-neutrinos are really something else entirely, called mirror neutrinos, with a mass different in a very systemic way from the mass of regular neutrinos, the lightest of which has a mass the corresponds to the temperature of the cosmic microwave background radiation. This is particularly notable because discovering that neutrinos had mass was something that the Standard Model didn't provide for at the time that this was discovered and I'm not aware of mainstream physics models that call for mirror neutrinos with masses different from regular neutrinos at all, despite the fact that we not only observe them but have a neat little formula to predict their masses.

Incidentally, we've also developed formulas that theoretically predict the relationship of the masses of different flavors of electrons, different flavors of neutrinos and different flavors of mirror neutrinos to each other.